In finance, an exotic option is a derivative which has features making it more complex than commonly traded products (vanilla options). These products are usually traded over-the-counter (OTC), or are embedded in structured notes.
Consider an equity index. A straight call or put, either American or European would be considered non-exotic (vanilla). An exotic product could have one or more of the following features:                The payoff at maturity depends not just on the value of the underlying index at maturity, but at its value at several times during the contract's life (it could be an Asian option depending on some average, a lookback option depending on the maximum or minimum, a barrier option which ceases to exist if a certain level is reached or not reached by the underlying, a digital option, peroni options, range options, etc.)        It could depend on more than one index (as in a basket options, Himalaya options, Peroni options, or other mountain range options, outperformance options, etc.)        There could be callability and putability rights.        It could involve foreign exchange rates in various ways, such as a quanto or composite option.        
Even products traded actively in the market can have the characteristics of exotic options, such as convertible bonds, whose valuation can depend on the price and volatility of the underlying equity, the credit rating, the level and volatility of interest rates, and the correlations between these factors.
Examples of exotic options include:
Barrier
CPPI
Cliquet
Compound option
Digital/Binary option
Lookback
Peroni Options
Rainbow option
Timer call
Unit Contingent Options
Variance swap
Bermudan options
A binary option is a type of option where the payoff is either some fixed amount of some asset or nothing at all. The two main types of binary options are the cash-or-nothing binary option and the asset-or-nothing binary option. The cash-or-nothing binary option pays some fixed amount of cash if the option expires in-the-money while the asset-or-nothing pays the value of the underlying security. Thus, the options are binary in nature because there are only two possible outcomes. They are also called all-or-nothing options, digital options (more common in forex/interest rate markets), and Fixed Return Options (FROs) (on the American Stock Exchange).
For example, a purchase is made of a binary cash-or-nothing call option on XYZ Corp's stock struck at $100 with a binary payoff of $1000. Then, if at the future maturity date, the stock is trading at or above $100, $1000 is received. If its stock is trading below $100, nothing is received.
In the popular Black-Scholes model, the value of a digital option can be expressed in terms of the cumulative normal distribution function.
Binary option contracts have long been available Over-the-counter (OTC), i.e. sold directly by the issuer to the buyer. They were generally considered “exotic” instruments and there was no liquid market for trading these instruments between their issuance and expiration. They were often seen embedded in more complex option contracts.
In 2007, the Options Clearing Corporation proposed a rule change to allow binary options, and the Securities and Exchange Commission approved listing cash-or-nothing binary options in 2008. In May 2008, the American Stock Exchange (Amex) launched exchange-traded European cash-or-nothing binary options, and the Chicago Board Options Exchange (CBOE) followed in June 2008. The standardization of binary options allows them to be exchange-traded with continuous quotations.
Amex offers binary options on some ETFs and a few highly liquid equities such as Citigroup and Google. Amex calls binary options “Fixed Return Options”; calls are named “Finish High” and puts are named “Finish Low”. To reduce the threat of market manipulation of single stocks, Amex FROs use a “settlement index” defined as a volume-weighted average of trades on the expiration day.
CBOE offers binary options on the S&P 500 (SPX) and the CBOE Volatility Index (VIX). The tickers for these are BSZ and BVZ, respectively. CBOE only offers calls, as binary put options are trivial to create synthetically from binary call options. BSZ strikes are at 5-point intervals and BVZ strikes are at 1-point intervals. The actual underlying to BSZ and BVZ are based on the opening prices of index basket members.
Both Amex and CBOE listed options have values between $0 and $1, with a multiplier of 100, and tick size of $0.01, and are cash settled.
Still, as of yet, the exotic options trading platforms available are limited and cumbersome. Therefore, a more flexible and easier to use platform for trading these options would be desirable.